Position sensing device

ABSTRACT

A position sensing device for measuring a position, comprises a position sensing device for measuring a position; a plurality of sensors arranged to produce sense signals each being a function of an input phase representative of a position to be measured; a combiner circuit arranged to generate an error signal by combining the sense signals according to an array of weight factors; a processing block including a loop filter to filter the error signal and arranged to output a phase value representative of the position; and a feedback loop comprising a feedback signal unit arranged for receiving the output phase value and for adjusting based on the received output phase value of the array of weight factors.

FIELD OF THE INVENTION

The present invention is generally related to the field of positionsensors, whereby position is defined by a linear displacement, arotation angle etc.

BACKGROUND OF THE INVENTION

Position sensors, for example angular position sensors for measuring anangular position of a sensor (e.g. mounted to a stator) relative to asource of a magnetic field (e.g. a magnet mounted to a rotor), are knownin the art. By measuring the strength of the magnetic field at variouslocations and/or in various directions, the position or orientation ofthe magnet(s) relative to the sensor elements can be determined.Position sensors, in which the magnetic field is generated by anexcitation coil are also known in the field, e.g. resolvers which havean excitation coil integrated in a rotor and sensing coils in a stator.Furthermore, position sensors are known which rely on detecting themagnetic field associated with eddy currents, e.g. eddy currents beinggenerated in a moving target consisting of conductive material.

Position sensors providing a digital output representative of the sensedposition are known in the art and are in many applications preferredover corresponding sensors, which only provide an analog output.

US2016/363638 discloses a magnetic field sensor for angle detection witha phase-locked loop that receives a measured magnetic field signalformed from sensing element output signals of a plurality of magneticfield sensing elements in response to a magnetic field. The phase-lockedloop is configured to generate an angle signal having a value indicativeof the angle of the magnetic field. The sensing elements are scannedsequentially, thus obtaining a sequence of readout values of individualsensing elements that, as a function of time, form a single measuredmagnetic field signal. During each readout time slot, only a singlesensing element is being read out. Consequently, the signal-to-noiseratio during one readout time slot is determined by a single sensingelement. Furthermore, the measured magnetic field signal then has theproperty that the process can be reversed, i.e. with knowledge of theapplied scanning scheme it is possible to deduce the readout value ofeach individual sensing element.

Hence, there is a need for a position sensing device that works fasterand yields a better signal-to-noise ratio.

SUMMARY OF THE INVENTION

It is an object of embodiments of the present invention to provide for aposition sensing device capable of providing a digital outputrepresentative of the sensed position.

The above objective is accomplished by the solution according to thepresent invention.

In a first aspect the invention relates to a position sensing device formeasuring a position, comprising

a plurality of sensors arranged to produce sense signals each being afunction of an input phase representative of a position to be measured,

a combiner circuit arranged to generate an error signal by combining thesense signals according to an array of weight factors,

a processing block comprising a loop filter to filter said error signal,wherein the processing block is further arranged for deriving from thefiltered error signal a phase value representative of the position andfor outputting the phase value representative of the position,

a feedback loop comprising a feedback signal unit arranged for receivingthe output phase value and for adjusting based on the received outputphase value the array of weight factors, so that the weight factors area function of the output phase value.

The proposed solution allows for reading out an estimated signalindicative of the position to be measured with reduced latency and agood noise performance. The position is typically a linear positionand/or a rotation angle. The processing block processes a combination ofmultiple sense signals at the same time, i.e. in a parallel way. Inother words, at any time instant, the signal being processed is acombination of the various sense signals, wherein the information ofeach signal contribution is merged in a way that, as a rule, cannot bereversed. The processing in parallel allows for a low position/angleerror when the input position/angle changes with high (angular) speed.In the invention an error estimate is obtained during each readouttime-slot. So for the same readout speed, this approach is faster inproducing an error estimate than the prior art solutions where thevarious sensing elements are scanned and processed sequentially. Theparallel readout also positively affects the noise performance. Thesensors provide their signal at every time instant. The sensor signalsare combined in a weighted way in the combiner circuit, where thedifferent noise contributions of sensors are averaged out, leading to anoutput with better signal-to-noise (SNR) compared to the SNR of anindividual sensing element signals. In other words, the parallel readoutof the sensors allows averaging the noise at each time instant.

In embodiments the processing block comprises a quantizer arranged toreceive the filtered error signal and to generate the phase valuerepresentative of the position.

In embodiments the error signal is an analog signal. In such case theloop filter of the processing block preferably comprises an analogfilter arranged to receive said error signal and to output a low-passfiltered version of the error signal. In preferred embodiments theanalog filter comprises an analog integrator for outputting a version ofthe error signal accumulated over time.

In advantageous embodiments the processing block comprises ananalog-to-digital converter for digitizing the continuous time errorsignal and/or the low-pass filtered error signal.

Preferably the loop filter of the processing block comprises a digitalfilter. In preferred embodiments the digital filter comprises a digitalintegrator.

In preferred embodiments the feedback signal unit comprises anangle-to-gain conversion block arranged for receiving the output phasevalue.

In embodiments of the invention the position sensing device comprisesone or more digital gain control units arranged to adapt said weightfactors. In certain embodiments the position sensing device comprisesone or more analog multiplexers to implement the array of weightfactors. In certain embodiments the position sensing device comprisescomponents which can be switchably connected to implement the array ofweight factors.

The sensors are in preferred embodiments magnetic sensors. They can beHall elements, giant magnetoresistance or tunneling magnetoresistancesensing elements. They can also be detection coils that sense atime-varying magnetic field. The sensors are preferably arranged formeasuring an angle of a magnetic field.

In an embodiment the plurality of sensors comprises at least threesensors arranged to produce sense signals each being a differentfunction of an input phase representative of a position to be measured.

In an aspect the invention relates to an arrangement comprising aposition sensing device as previously described and a multi-pole magnet.

In another aspect the invention relates to a position sensing device formeasuring a position, comprising

a plurality of sensors arranged to produce sense signals each being afunction of an input phase representative of a position to be measured,

a combiner circuit arranged to generate an error signal by combiningsaid sense signals according to an array of weight factors,

a processing block comprising a loop filter to filter said error signal,said loop filter comprising a cascade of an analog filter, ananalog-to-digital converter and a digital filter, and further comprisinga quantizer arranged to receive said filtered error signal and toproduce from said filtered error signal a quantizer output signal,

a feedback loop comprising a feedback signal unit arranged for receivingsaid quantizer output signal and for adjusting based on said receivedquantizer output signal said array of weight factors, so that saidweight factors are a function of said quantizer output signal,

a noise canceling block arranged for combining said quantizer outputsignal with a digital signal upstream of said quantizer such that thecombined signal provides an improved phase value representative of saidposition and having a reduced dependence on quantization noise caused bysaid quantizer.

In a preferred embodiment the noise canceling block comprises a firstrecombination filter arranged to receive said quantizer output signal, asecond recombination filter arranged to receive a digital signal outputby said analog-to-digital converter and an adder circuit for addingoutputs of said first and said second recombination filter, wherein saidfirst and said second recombination filter are selected to obtain animproved phase value representative of said position being lessdependent on quantization noise caused by said quantizer than the signalat the quantizer output.

In a preferred embodiment the analog filter of the loop filter has atransfer function substantially equal to the ratio of the firstrecombination filter's transfer function and the second recombinationfilter's transfer function. In case the analog filter transfer functionexactly equals said ratio, the quantization noise contribution iscompletely eliminated. However, even if there is a relative deviation Δbetween the analog filter transfer function and the ratio, there isstill an important reduction of the quantization noise caused by thequantizer, provided the relative deviation Δ remains moderate, e.g|Δ|<10%.

Preferably the first recombination filter and/or said secondrecombination filter are adaptive. Preferably the first recombinationfilter and/or second recombination filter are adapted to remove adependency of the analog-to-digital converted output signal from thequantization noise of the quantizer determined in the digital domain. Ina specific embodiment the quantization noise is determined by digitallysubtracting the input of the quantizer from its output. The firstrecombination filter and/or the second recombination filter may have aprogrammable gain. The analog-to-digital converter advantageouslycomprises a gain controller unit to determine that programmable gain.

In embodiments of the invention the quantizer has a lower resolutionthan the analog-to-digital converter. This is particularly advantageousfor reducing the complexity associated with the combiner block.

In certain embodiments the position sensing device comprises a delaycompensation filter to compensate for a delay introduced, for example,by said first recombination filter.

In preferred embodiments the analog-to-digital converter is aSigma-Delta modulator comprising a second quantizer embedded in aninternal feedback loop containing a further analog filter and a feedbackdigital-to-analog converter.

Advantageously the first recombination filter and/or secondrecombination filter are Finite Impulse Response filters. In a specificembodiment the first recombination filter is a FIR filter proportionalto the numerator polynomial in z⁻¹ of H_(a)(z), and/or B(z) is a FIRfilter proportional to the denominator polynomial in z⁻¹ of H_(a) (z).

For purposes of summarizing the invention and the advantages achievedover the prior art, certain objects and advantages of the invention havebeen described herein above. Of course, it is to be understood that notnecessarily all such objects or advantages may be achieved in accordancewith any particular embodiment of the invention. Thus, for example,those skilled in the art will recognize that the invention may beembodied or carried out in a manner that achieves or optimizes oneadvantage or group of advantages as taught herein without necessarilyachieving other objects or advantages as may be taught or suggestedherein.

The above and other aspects of the invention will be apparent from andelucidated with reference to the embodiment(s) described hereinafter.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will now be described further, by way of example, withreference to the accompanying drawings, wherein like reference numeralsrefer to like elements in the various figures.

FIG. 1 illustrates a generic scheme of a position sensing deviceaccording to the invention.

FIG. 2A illustrates an embodiment of a position sensing device of thisinvention where the sensed magnetic fields are due to a rotating magnet.FIG. 2B illustrates an embodiment of the position sensing device wherethe sensed magnetic fields are due to eddy currents being induced by anexcitation coil in a movable metal target.

FIG. 3 illustrates a possible implementation of a digitally controlledgain.

FIG. 4 illustrates more in detail a possible implementation of an analogmultiplexer and switching components.

FIG. 5 illustrates practical weighting schemes with two and fourprojection signals, respectively.

FIG. 6 illustrates an embodiment of the position sensing device whereina spinning scheme is applied.

FIG. 7 illustrates a stray field robust arrangement for use with a6-pole magnet.

FIG. 8 illustrates a position sensor providing an A/D conversion of theinput angle according to the invention with improvement of the digitaloutput through cancelation of the quantization noise.

FIG. 9 shows a behavioral model of the position sensor of FIG. 8 andillustrates a possible choice for the recombination filters A(z) andB(z) when the analog filter Ha introduces delay, and the use of adelay-compensating filter C(z).

FIG. 10 illustrates two possible implementations of a delay compensationfilter.

FIG. 11 illustrates an embodiment with inner-loop noise shaping appliedfor the analog-to-digital converter.

FIG. 12 illustrates an embodiment with adaptive gain correction.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

The present invention will be described with respect to particularembodiments and with reference to certain drawings but the invention isnot limited thereto but only by the claims.

Furthermore, the terms first, second and the like in the description andin the claims, are used for distinguishing between similar elements andnot necessarily for describing a sequence, either temporally, spatially,in ranking or in any other manner. It is to be understood that the termsso used are interchangeable under appropriate circumstances and that theembodiments of the invention described herein are capable of operationin other sequences than described or illustrated herein.

It is to be noticed that the term “comprising”, used in the claims,should not be interpreted as being restricted to the means listedthereafter; it does not exclude other elements or steps. It is thus tobe interpreted as specifying the presence of the stated features,integers, steps or components as referred to, but does not preclude thepresence or addition of one or more other features, integers, steps orcomponents, or groups thereof. Thus, the scope of the expression “adevice comprising means A and B” should not be limited to devicesconsisting only of components A and B. It means that with respect to thepresent invention, the only relevant components of the device are A andB.

Reference throughout this specification to “one embodiment” or “anembodiment” means that a particular feature, structure or characteristicdescribed in connection with the embodiment is included in at least oneembodiment of the present invention. Thus, appearances of the phrases“in one embodiment” or “in an embodiment” in various places throughoutthis specification are not necessarily all referring to the sameembodiment, but may. Furthermore, the particular features, structures orcharacteristics may be combined in any suitable manner, as would beapparent to one of ordinary skill in the art from this disclosure, inone or more embodiments.

Similarly it should be appreciated that in the description of exemplaryembodiments of the invention, various features of the invention aresometimes grouped together in a single embodiment, figure, ordescription thereof for the purpose of streamlining the disclosure andaiding in the understanding of one or more of the various inventiveaspects. This method of disclosure, however, is not to be interpreted asreflecting an intention that the claimed invention requires morefeatures than are expressly recited in each claim. Rather, as thefollowing claims reflect, inventive aspects lie in less than allfeatures of a single foregoing disclosed embodiment. Thus, the claimsfollowing the detailed description are hereby expressly incorporatedinto this detailed description, with each claim standing on its own as aseparate embodiment of this invention.

Furthermore, while some embodiments described herein include some butnot other features included in other embodiments, combinations offeatures of different embodiments are meant to be within the scope ofthe invention, and form different embodiments, as would be understood bythose in the art. For example, in the following claims, any of theclaimed embodiments can be used in any combination.

It should be noted that the use of particular terminology whendescribing certain features or aspects of the invention should not betaken to imply that the terminology is being re-defined herein to berestricted to include any specific characteristics of the features oraspects of the invention with which that terminology is associated.

In the description provided herein, numerous specific details are setforth. However, it is understood that embodiments of the invention maybe practiced without these specific details. In other instances,well-known methods, structures and techniques have not been shown indetail in order not to obscure an understanding of this description.

The present invention relates to a position sensor. Position may referto a linear displacement, a rotation angle, etc. The proposed positionsensing device can for example be used for high rotation speeds up to80000 rpm and is capable of tracking the rotation angle at any constantrotation speed with only a small error, e.g. less than ±2°. The positionsensing device comprises a plurality of sensors that produce a pluralityof analog sensing signals on which the device operates in a trackingmode in order to track the position. A tracking loop keeps track of anexternal displacement/angle in an incremental way, based on comparing a‘predicted’ output to the actual phase/position/angle.

In preferred embodiments the position sensing device is an angularsensor using an external magnet. In other embodiments the positionsensor is an angular sensor (an electrical resolver) based on mutualinductance. In yet other embodiments the position sensor is a linearposition sensor, e.g. based on a magnet or on an electrically excitedcoil being linearly displaced relative to the sensor.

In any of the envisaged sensor types a generalized position is to bemeasured, e.g. a linear position or an angle. Two or more sense signalsare available, e.g. cos θ_(i) and sin θ_(i), in which the phase/angleθ_(i) changes as a function of the (generalized) position.

An input phase θ_(i) is associated with the position to be measured. Thesensor system comprises N≥2 sensing elements (i.e. at least two)providing analog sensing signals representative of the input phase/angleθ_(i). These sensing signals can, for instance, be represented as

$\begin{matrix}{{{S_{k}\left( \theta_{i} \right)} = {{A\; {\cos \left( {\theta_{i} - {k\frac{2\; \pi}{N}}} \right)}\mspace{14mu} k} = 0}},1,{{\ldots \mspace{14mu} N} - 1}} & (1)\end{matrix}$

with A denoting the amplitude of the sensing element signals. As can beseen from equation 1, each sensing signal has a different phase, whichin this case is a function of the input phase/angle θ_(i) and theposition of the HE element with respect to a reference.

A subclass of the proposed position sensors are angular sensors, inwhich case the input phase θ_(i) may be the same as the mechanicalrotation angle θ_(mech). The input phase θ_(i) may also be a linearfunction of the mechanical rotation angle. Alternatively, it may be anon-linear function of the mechanical rotation angle, in which caseadditional corrections of the nonlinearity may be included

A subclass of the proposed position sensors are linear position sensors,in which case the input phase θ_(i) may be a linear function of themechanical displacement x_(mech), e.g. θ_(i)=k·x_(mech) with k someproportionality factor. An extra constant φ₀ may be present as well.Also here, the input phase may be a non-linear function of themechanical displacement, in which case additional corrections of thenon-linearity may be included.

A subclass of the proposed position sensors are magnetic positionsensors which, for instance, measure the displacement of a magneticfield (e.g. generated by a magnet or an excitation coil) with respect tothe position sensor.

A subclass of the proposed angular sensors are magnetic angle sensorswhich measure the angle of a magnetic field e.g. generated by a magnet.In this subclass the sensing elements may be based on horizontal orvertical Hall elements, giant magnetoresistance (GMR) or tunnellingmagnetoresistance (TMR) sensing elements, etc. This may be incombination with a magnetic layer (e.g. an integrated magneticconcentrator (IMC)) that locally alters the magnetic field, e.g. changeits direction, e.g. from an in-plane magnetic field to a verticalmagnetic field. In the magnetic case the sensing element signals as inequation (1) can also be interpreted as projections of the magneticfield in different directions, e.g. along the directions identified bythe angles k·2π/N for k=0, 1, . . . , N−1. When also a magnetic layer isinvolved, the shape of the magnetic layer may be chosen to obtainprojections.

In a subclass of the proposed angular sensors a plurality of sensingelement signals is obtained as the output of an electrical resolverhaving at least N≥2 sensing coils. These electrical resolvers typicallyrely on an angle dependent mutual inductance between a driving coil andthe different sense coils.

In a subclass of the proposed angular sensors a plurality of sensingelement signals is obtained as the output of at least N≥2 sensing coilswhich pick up the magnetic field from eddy currents induced in aconductive target. These eddy currents can for instance be induced inthe target by means of a coil driven by an alternating electricalexcitation. The shape of the conductive target is such that a rotationor displacement of the target relative to the sensing coils leads to anangle-dependent or displacement-dependent change of the sensing coilsignals.

A general block scheme of an embodiment of the position sensing deviceof this invention is shown in FIG. 1. The generalized position to bemeasured, represented by an input phase θ_(i), affects the output of atleast two sensors (2). The resulting sense signals are fed to thecombiner circuit (4), where the signals S_(k) are each multiplied withtheir corresponding weight factor G_(k). The resulting weighted sumsignal (5) next goes to the processing block (6), where it is filteredin a loop filter (60) and an estimate of the output phase θ_(o) (7) isobtained. The signal produced by the combiner circuit is a signalrepresentative of the error between the input phase θ_(i) and theestimated output phase θ_(o). The output phase θ_(o) (7) is fed to afeedback signal unit (8) where a phase-to-weight conversion is performedand updated weight factors are determined for use in the next iteration.

The processing block (6) processes a combination of the various sensesignals at the same time, i.e. in a parallel fashion. This processing inparallel allows for a low position/angle error when the inputposition/angle changes with high (angular) speed. An error estimate isobtained during each readout time-slot, thus, for the same readoutspeed, faster than when adopting a sequential approach. As the sensorsignals are combined in the combiner circuit, the different noisecontributions of sensors are averaged out, leading to an output withbetter signal-to-noise (SNR) compared to the SNR of an individualsensing element signal. In other words, the parallel readout of thesensors allows averaging the noise at each time instant. The readout ofa sensing element may also comprise averaging and/or combining theoutcomes of measurements over different phases, such as is for instancethe case when applying spinning current averaging in Hall readout. Suchcombining/averaging may take place within each time-slot. Each sensesignal may then correspond to an averaged/combined value of readouts ona same sensing element. Also in this case, the same conclusion holdsthat a parallel processing of the thus obtained sense signals allows forbetter SNR and/or faster error estimates compared to a sequentialprocessing.

FIG. 1 details the overall structure of the position sensing deviceaccording to the present invention and clarifies signals involved at thesystem level. The signals in this scheme may be analog signals, digitalsignals or even any other type of signals that carry a similar kind ofinformation as the signals appearing in the general block diagram. Forexample, signals received from sensing elements may be in the digitaldomain, e.g. when these sensing elements are by themselves moresophisticated systems that comprise a means for conversion to thedigital domain. In the latter case the combiner circuit, processingblock and phase-to-weights conversion block may be completely in thedigital domain.

A practical embodiment is illustrated in FIG. 2A. In this example anangle sensor is considered based on a measurement of the direction of amagnetic field, e.g. generated by a permanent magnet. Furthermore, Hallelements are used as primary sensing elements in this embodiment. Themain signal path in FIG. 2A must comprise at least two Hall plates. Inthis particular case there are eight Hall plates. In FIG. 2A they areevenly spread over a full circle. In other embodiments they may beevenly spread over only a part of a circle or not evenly spread. Theactual spreading affects how the weights are adapted as a function ofthe output angle. Some configurations may be in that sense preferableover other configurations, because they lead to simpler relations.

The combiner circuit (4) in FIG. 2A generates a weighted combination ofHall element (HE) signals. Hence, each HE signal is multiplied with aweight factor corresponding to that HE signal. Hence, the number ofweight factors equals the number of sensor signals, in this particularexample HE signals. The resulting signal (5) is next filtered in aprocessing block (6). Details on the filtering are provided below. Thereshould be at least two linearly independent sensor signals, i.e. atleast two sensor signals can be identified which are not simplyproportional to each other. In other words, there are at least twodifferent functions involved, where a ‘different function’ can also be asame function, e.g. a cosine function, but with a different argument,e.g. an argument which is a different combination of the input phase anda fixed phase. This can also be seen as sensing in at least twodifferent directions, e.g. in the case of a magnetic field the sensorssense projections of the magnetic field in different directions, forexample in the plane of the sensor, with an angle of 45° and with anangle of 90°. The processing block (6) then outputs a phase value θ_(o)(7) representative of the position to be determined. The feedback signalunit (8) in the feedback loop is fed with the phase value output by theprocessing block and determines updated values of the various weightfactors in the array. These updated weight values are then used when thenext array of sense signals comes in. The resulting weighted signal isso indicative of the present error between the input phase θ_(i) and theoutput angle θ_(o).

The combiner circuit (4) in FIG. 2A generates a weighted combination ofHall element (HE) signals in the analog domain. It is advantageous tohave an analog filter (61) providing analog low-pass filtering in thedevice, as this yields low noise and implicit anti-aliasing filtering.The analog filter (61) may be for instance a continuous-time analogintegrator. The ADC (62) converts the integrator output, which for theshown system is representative of the angular speed, to the digitaldomain. The digital filter (63), in this embodiment a digitalintegrator/accumulator with an added feedforward path to improve thestability of the tracking loop, converts the digital ADC signal into anangle. Alternatively, the tracking loop stability can also be improvedby proper choice of the analog filter, e.g. by adding a zero to thetransfer function, e.g. in case of an integrator implemented by adding aresistor in series with the capacitor used in the integrator. In thisparticular example, the combination of the analog filter (61), the ADC(62) and the digital filter (63) constitute the loop filter (60)receiving at its input a continuous-time signal from the combinercircuit. Next this angle is quantized, whereby an angle at its input isrounded/truncated/mapped to an output angle belonging to a finite set ofpossible angles. The finite set may contain integer multiples of a basicangle, e.g. multiples of 22.5° (corresponding to 4 bits), but this isnot required. The mapping may be stochastic in nature, e.g. involvingthe use of dither (i.e. an intentionally applied form of noise), e.g. torandomize quantization errors. In the feedback loop a digital mapping isperformed, e.g. implemented as a lookup table or digital logic, fortranslating the quantized angle to an array of N gain coefficientsG_(k), which determine the weights used in the combiner circuit.

In another exemplary embodiment, illustrated in FIG. 2B, the workingprinciple of the angle sensor is based on sensing the magnetic field ofeddy currents in a movable metal target. In this embodiment a changingmagnetic field is generated by means of an excitation coil being fedwith an alternating current. The alternating current may be derived froman oscillator circuit. An efficient solution is to use the excitationcoils self-inductance L in combination with a tank capacitance C as partof an LC oscillator. By operating the excitation coil at resonance, thecurrent through is effectively boosted by the quality factor of theresonant tank. The time-varying current in the excitation coil thengenerates a time-varying magnetic field that induces eddy currents in arotatable metal target. These eddy currents rise and fall at the samerate as the excitation field. The magnetic field generated by the eddycurrents is therefore also time-varying at the same frequency. Thechanging magnetic field associated with the time-varying eddy currentsinduces voltages in a number of sensing coils. In the present examplethree sensing coils oriented 120° apart are used. The metal target shapeis such that when rotating the target, the coupling between the targetand the individual sensing coils changes (i.e. is a function of therotation angle). The amplitude of the different sense-coil signals thusbecome a function of the rotation angle. Because the time-varyingmagnetic fields generated by the eddy current are also at the oscillatorfrequency, the sense-coil signals can be demodulated using theoscillator signal(s) to extract the amplitude information. This thenprovides a multitude of sense signals with a phase representative forthe rotation angle of the target. Similar to the embodiment of FIG. 2A,the combiner circuit (4) in FIG. 2B generates a weighted combination ofthe demodulated sense signals in the analog domain. The rest of thebuilding blocks in FIG. 2B are similar in purpose and functionality tothose in FIG. 2A. A variant of the present embodiment (not shown), iswhen the combiner circuit (4) operates directly on the sense coilsignals (without demodulation) and the output of the combiner circuit(4) is then demodulated.

The various building blocks of the position sensing device of theinvention are now discussed more in detail. For ease of description,below the focus is on an angular position sensor. However, it is to beunderstood that any reference to an “angle” in this description may needto be translated into alternative terms in case of other positionsensors. For instance, “angle” may need to be replaced by “phase” or“phase representative of a position”.

Combiner Circuit

The combiner circuit is a key component of the proposed device. Its taskis to provide a measure of the difference between the input angle θ_(i)and the output angle θ_(o), i.e. an estimate of the input angle.However, since the input angle θ_(i) is not directly available, butrather encoded as a set of trigonometric values that represent theprojections of the magnetic field angle θ_(i) on a multitude of axes,this needs to be obtained in an indirect way. Referring to FIG. 2A, thecombiner circuit (4) actually makes a linear combination of HE signalsmultiplied by the weights, i.e. Σ_(k=0) ^(N-1)G_(k)×HE_(k). The weightsG_(k) used in this expression are—by construction—function of the outputangle θ_(o), i.e. G_(k)=G_(k)(θ_(o)). The combiner applies the array ofweights to the set of individual sensor signals and combines (adds)these weighted contributions to produce an output representative of theangle/phase difference.

In general, the functions G_(k)(θ_(o)) defining the various weightcoefficients of the array as a function of the output angle may bedetermined as follows. A single value θ is considered from the set ofpossible output angles. The N sensor elements signals S_(k)(θ) aredetermined when the input angle θ_(i) is equal to the considered outputangle value θ. A set of non-zero values G_(k)(θ) (k=0, . . . , N−1) canthen be found to solve the linear equation Σ_(k=0)^(N-1)G_(k)(θ)×S_(k)(θ)=0. This homogeneous linear equation has aninfinite number of solutions, which means this freedom can be exploited,e.g. for optimizing the combiner circuit performance. A possibleoptimization is explained next. For this, the N sensor elements signalsS_(k) are considered when θ_(i) is close to θ, but may deviate from itby an amount x, i.e. the input angle θ_(i) is equal to θ+x. For xsufficiently small, the sensing element signals can be expanded as

S _(k) =S _(k)(θ)+S _(k)′(θ)·x+n _(k) k=0 . . . (N−1)  (2)

with S′_(k) denoting the derivative of the k^(th) sensor signal withrespect to angle/phase changes, and n_(k) denoting the noise of thek^(th) sensing element. A set of gain coefficients G_(k) can be foundfor this particular output angle θ for which the output of the combinercircuit has good (optimal) signal-to-noise ratio (SNR). The output ofthe combiner circuit can be written as:

$\begin{matrix}{{\sum\limits_{k = 0}^{N - 1}{G_{k}S_{k}}} = {\underset{\underset{= 0}{}}{\sum\limits_{k = 0}^{N - 1}{G_{k}{S_{k}(\theta)}}} + {\left( {{\sum\limits_{k = 0}^{N - 1}G_{k}},{S_{k}^{\prime}(\theta)}} \right) \cdot x} + {\sum\limits_{k = 0}^{N - 1}{G_{k}n_{k}}}}} & (3)\end{matrix}$

Assuming the noise components n_(k) are uncorrelated and have equalvariance, a set of optimum gains G_(k) that maximize the output SNR canbe derived analytically. One set of optimal weights can be shown to be:

$\begin{matrix}{{{G_{k}(\theta)} = {\frac{d}{d\; \theta}\left( \frac{S_{k}(\theta)}{\sqrt{\frac{2}{N}{\sum\limits_{k = 0}^{N - 1}{S_{k}^{2}(\theta)}}}} \right)}},{k = {0\mspace{14mu} \ldots \mspace{14mu} \left( {N - 1} \right)}}} & (4)\end{matrix}$

Other optimal weights can be obtained by applying a common scale factorto the above.

By repeating the above procedure for all possible output angles, one canobtain weight coefficients G_(k)(θ) for all angles θ from the set ofpossible output angles. This means that for any possible output angleθ_(o), the weight coefficients G_(k)(θ_(o)), (k=0, . . . , N−1) are welldefined.

In the case of sensing element signals given by expression (1), theoptimal weights of equation (4) are given by

$\begin{matrix}{G_{k} = {- {\sin \left( {\theta_{o} - {k\frac{2\; \pi}{N}}} \right)}}} & (5)\end{matrix}$

The optimal weights are in this case simple trigonometric functionsdepending on the output angle. With these weights, the combiner circuitoutput can be shown to be (for the considered case):

$\begin{matrix}{{\sum\limits_{k = 0}^{N - 1}{G_{k}S_{k}}} = {\frac{N}{2}{A \cdot {\sin \left( {\theta_{i} - \theta_{o}} \right)}}}} & (6)\end{matrix}$

hence the output signal of the combiner circuit is proportional tosin(θ_(i)−θ_(o)). Because the goal of the overall feedback loop is tolet the output angle θ_(o) track the input angle θ_(i), the differenceθ_(i)−θ_(o) is relative small (in tracking mode), and in goodapproximation one has sin(θ_(i)−θ_(o))=θ_(i)−θ_(o).

The combiner circuit provides an output which is related to theangle/phase difference, e.g. a signal proportional to sin(θ_(i)−θ_(o)).In certain respect this is similar to the output signal of a phasedetector in a PLL. However, while the output may be similar, thecombiner circuit is quite different from a classical phase detectorcircuit. Classical phase detector circuits operate on input signalshaving a non-zero frequency, i.e. they evolve in time even when thephases themselves remain constant. One classical phase detector is amultiplier that multiplies two sinusoidal or square-wave like inputsignals, in most cases followed by a filter that removes double- andhigher frequency tones. Other classical phase detectors rely ondetecting “events” in their input signals, such as the occurrence of anedge or a level-crossing. These classical phase detectors only measure aphase difference between non-stationary signals. This is also the casein the prior art angle sensor architectures US2016/363638 andUS2010/026287, in which a classical phase detector is used, having twoinput signals that change with time: a first one obtained bysequentially scanning a multitude of sensing elements at a predeterminedscanning clock frequency, and a second one generated by an oscillatorthat has a related clock signal, e.g. the scanning clock, as an input.The phase detector operates by measuring the time between edges of thetwo distinct input signals. The multiple sensing elements aresequentially scanned and, hence, all individual sensing element signalsremain available as a sequence of values, which in principle can bereversed. In contrast, in the present invention a parallel processing ofthe received sensor signals is adopted. For this purpose, the combinercircuit receives N>1 sensing signals at each instance in time and anequal number N of feedback signals (defining the weight of each sensingsignal). Therefore, the combiner circuit receives at least four signals,while a classical phase detector only receives two signals. Furthermore,in the present invention the input signals may be completely static (DC)signals (which occurs when θ_(i) and θ_(o) are constant), and still thecombiner circuit is able to provide an output representative for thedifference between θ_(i) and θ_(o).

The various weights G_(k) can be determined from the output angle bymeans of software-based calculations and/or by means of digital logic.In case the output angle is quantized, there is only a limited set ofpossible values. The various weights G_(k) can be predetermined and, forinstance, stored in a lookup table (81) (i.e. in digital form) in thefeedback loop as in FIG. 2.

The weights G_(k) can be implemented as a digitally controlled gain (82)as in the embodiments of FIG. 2A and FIG. 2B. These weights may thenrepresent gain factors (gain coefficients). There are various ways toimplement such digitally controlled weights. The digitally controlledweights/gains in the combiner circuit may be realized by providingswitchable components such as resistors, transconductances, capacitors,etc. The switchable components may be built using a common unitcomponent. The digitally controlled weights/gains in the combinercircuit may also be realized by an analog multiplexer, e.g. forinterconnecting one out of a number of sensing element signals to acomponent (resistor, transconductor etc.). The required functionalitymay also be merged with the next block of the system, which is in theexemplary angle-domain architecture of FIG. 2 an integrator.Conceptually, a voltage-domain integration can be split into avoltage-to-current conversion (i.e. a transconductance), followed by acurrent/charge integrator (typically using capacitors for accumulationof the charge associated with the input current). The digitallycontrolled weight can then for instance be realized by digitallycontrolling the transconductance with which the different HE signals areconverted into a current. For instance, switches can be added to atransconductor circuit that allow controlling a conversiontransconductance or (trans)resistance. In particular, one can deviseswitching schemes that rely on using identical unit components, since itis known that identical components are typically better matched. Apossible approach of using unit elements for obtaining an integratorwith accurately controlled weights is to split the total inputtransconductance of the integrator circuit into a number of identical(low-noise) transconductance units (LNTs), and using a digitallycontrolled analog multiplexer before each transconductance unit toselect one out of a number of sensing element signals, the selectionbeing dependent on the value of the output angle θ_(o). This isillustrated in FIG. 3, where the gain is digitally controlled byincreasing or decreasing the number of transconductance units being usedfor converting the HE signals into current. In some cases one can alsoapply a zero signal to the unit or disable it in some way, e.g. when acertain unit is not needed for a particular output angle θ_(o).

The functionality of the feedback signal unit (8) may be expanded togenerate control signals for setting the weights of the combiner circuit(4). These control signals may be a means for defining the state of allswitches that affect these weights, and/or for defining the state of themultiplexers utilized in the combiner circuit. Two mappings may then beimplemented in the feedback signal unit (8): a first one from the outputangle θ_(o) to the weight coefficients G_(k) and a second one from theweight coefficients G_(k) to the control signals. It is also possiblethat a combined mapping is implemented in the feedback signal unit, inwhich the control signals are generated more directly as a function ofthe output angle θ_(o). While conceptually the connection between thefeedback signal unit (8) and the combiner circuit (4) conveysinformation on the weight coefficients G_(k), e.g. as shown in FIG. 1,the actual physical form of this link may take many different forms,such as digital signals defining the states of the controlled elementsof the combiner circuit.

A more detailed view of the analog multiplexer and the switchingcomponents is provided in FIG. 4. This figure details a circuit-levelimplementation of an analog multiplexer that allows selecting one out oftwo possible differential sensing signals, being (VX+,VX−) and(VY+,VY−), and also allows selecting a zero differential signal byswitching the multiplexer's differential output nodes (Vin+,Vin−) to acommon voltage Vcm. The analog mux uses CMOS switches, which can beoperated by digital control voltages defining the states of theseswitches. The analog mux output is connected to the input of a low-noisetransconductor (LNT) unit. The LNT's input transistor receiving thedifferential voltage (Vin+,Vin−) and act as a source-follower for thisdifferential input voltage. The differential input voltage is thereforealso forced over the resistor R_(LNT) and a signal-dependent current isgenerated. Other transistors in the LNT unit are there to improve thesource-follower characteristic and to provide a (possibly scaled) copyof the signal-dependent current generated by the resistor R_(LNT). Atthe bottom of FIG. 4 it is shown how the same type of circuit can beeasily adapted to obtain a gain-programmable variant. In this, theR_(LNT) is composed of a number of identical resistor units Ru andswitches are inserted to put a certain number of these units inparallel. A series connection of resistors, with switches allowing toshort-circuit some elements (not shown on the figure) could also be usedto create a variable resistance R_(LNT). It is clear that by controllingthe resistance R_(LNT) the circuit operates as a gain-programmabletransconductance.

Embodiments of the combiner circuit may include any known technique usedin integrated circuits design to compensate for component mismatch. Thisincludes the use of calibration and/or trimming as well as the use ofdynamic element matching techniques, e.g. allowing variation of thecombination of units being used for realizing a particular weightfactor.

The weights G_(k) can be positive for some θ_(o) angles, but can benegative for other output angles. The sign of the weight G_(k) can beimplemented in a number of ways. For instance, when the sensing elementsignals are differential, the sign can be changed by swapping theconnections. Alternatively, some sensing elements, like Hall elements,allow changing the sign by changing the bias current flow direction.This is also illustrated in FIG. 3. For single-ended sensing signals asign reversal may be realized by an inverting amplifier configuration.

In practical circuit implementations the different weights can be moreeasily implemented if they can be composed from a number of identicalunits. In such cases the weight coefficients are necessarily quantizedand may deviate from the theoretical values given above. As a result ofthis weight quantization, the combiner output may deviate from the idealcase and may become non-zero for input angles which ideally would give azero output. Since the combiner output is interpreted in thearchitecture as an error between input and output angle, it can beunderstood that the weight quantization may have an impact on theoverall accuracy of the sensor system. Fortunately, this can be remediedby shifting the output angle θ_(o) corresponding to a particular weightcombination. The shifted value is defined as the angle θ_(o) which, whenthe same input angle is applied (i.e. θ_(i)=θ_(o)), makes the linearcombination equal to zero. This method allows taking the effects ofweight quantization into account by making (small) corrections to theoutput angle which would apply in the absence of weight quantization.This can be easily done when the processing block comprises an anglequantizer block, since in this case the correction can be accomplishedby a change of the allowed quantization levels. Simulations show thatwith such adaptations the system can operate satisfactorily, with thedeviations having little or no impact on the performance. Of course, theangle quantizer block might become somewhat more involved. For instance,it is more complex to find a closest value in a non-uniform set ofallowed values compared to a uniform set.

In FIG. 5 two practical weighing schemes are presented that can beimplemented with units and that still lead to correct system operation.In both schemes the above described corrections for eliminating theeffects of weight quantization have been made and one can see thatindeed not all the discrete output angles θ_(i) are perfect integermultiples of a single base angle. Surprisingly, when using moreprojection signals, e.g. the scheme shown on the right side of FIG. 5,the above corrections are not needed because the levels remain exactlyat their theoretical value, in spite of the weights having been roundedto convenient values. Hence, the allowed output angles remain simpleinteger multiples of a base angle (π/8), which makes the angle quantizerblock simpler to implement.

Additional methods for realizing weighting coefficients exist. E.g., incases where Hall elements are used as sensing elements, it is possibleto realize a weight factor by modulation of the HE bias currents (orbias voltages) in a way depending on the output angle. This offers theadvantage that it is fairly easy to implement, e.g. using a current DACfor defining the bias current.

Combined solutions wherein distinct methods for introducing weightingcoefficients are used together, are also possible. For instance, adigitally controlled gain by switching a number of transconductor unitsto particular sensor signals, can be adjoined with means to regulate thebias current (or voltage) of the sensing elements.

Analog Filter Comprising an Integrator

As illustrated in FIG. 2, in the processing block (6) an analog filter(61) comprising an integrator receives as its input the output of thecombiner circuit (4) representative of an error signal, e.g.proportional to sin(θ_(i)−θ_(o)). As explained above, when in trackingmode, the error signal (5) is representative of the angle/phase errorθ_(i)−θ_(o). The integrator output, being the integral of this errorsignal, therefore represents an accumulation over time of theangle/phase error of the output relative to the input. Since the overalltracking loop can be made to operate in a stable way, the integratorstate remains bound at all times. This implies that the average errorbecomes asymptotically zero as time progresses, which explains animportant feature of the proposed architecture: the output angle is, onaverage, an accurate representation of the input angle.

It is not absolutely required to use an integrator for processing theangle/phase error signal. This may also be a (low-noise) amplifier thatprovides gain, or a more general class of analog low-pass filters.Another example is the addition of a series resistor in the feedbackpath of an integrator circuit to add a zero to the loop filter, e.g. forenhanced stability of the loop. In order to arrive at the abovementionedfeature that the average output equals the average input, one or moreintegrations are needed in the forward path of the device, i.e. in theloop filter. However, these integrations can be performed in otherblocks, e.g. in the digital filter(s) comprised in the loop filter asdiscussed later in this description.

However, the use of an analog low-pass filter, e.g. an integrator, forprocessing the error signal of the combiner circuit does bring someadvantages. A first benefit relates to the broadband noise of thesensing elements. Because the combiner circuit combines the inherentlynoisy sensing element signals, the output (5) (i.e. the angle errorsignal) also contains broadband noise. A continuous-time low-passfiltering of the error signal suppresses this broadband noise. Due tothis filtering effect, it is possible to sample the analog filter outputwith little extra noise aliasing. In other words, the analog integratorprovides an implicit anti-aliasing filtering. This is advantageous whenthe analog filter is followed by a sampling block, such as an ADC (seethe embodiment of FIG. 2) or a switched-capacitor circuit (e.g. forextra gain, additional filtering, . . . ). A second advantage is thatthe analog filter (61), especially when it comprising one or moreintegrators, provides noise shaping for quantization noise sourcespresent in the loop e.g. caused by the angle quantization block, and/orthe ADC (when present). A third advantage is that the analog filterprovides gain (and noise filtering) with little extra propagation delay.

Some sensing elements, such as Hall elements, have relatively largeintrinsic offsets, in which case current spinning is often applied toseparate the useful magnetic signal from the offset. It is possible tochoose the current spinning scheme such that the useful signal isup-converted, arriving at a chopped sensor signal. Instead of expression(1), the sensing signals may be represented with the use ofspinning/chopping as

$\begin{matrix}{{{S_{k}\left( \theta_{i} \right)} = {{\left( {- 1} \right)^{n}A\; {\cos \left( {\theta_{i} - {k\frac{2\; \pi}{N}}} \right)}} + V_{o,k}}}{{k = 0},1,{{\ldots \mspace{14mu} N} - 1}}} & (7)\end{matrix}$

in which (−1)^(n) denotes the alternating Hall signal due to the appliedspinning scheme (with n an integer indicating the n^(th) time slotduring which sensor signals are being read out) and V_(o,k) theindividual offset of sensing element k. This “chopped” sensor signal isthen connected to the front-end, e.g. to one or more LNT units in FIG.3. So, the signals processed by the combiner circuit can be composed ofan offset and possibly some flicker noise on the one hand and on theother hand the up-converted magnetic signal. The combiner circuit outputthen needs to be demodulated prior to integration. This demodulationprior to integration can be seen in the sensor system of FIG. 6 as asecond factor (−1)^(n).

In an inductive based position sensor the chopping operation may be dueto the modulation at high frequency used in the excitation coil. The(−1)^(n) might correspond to the use of an analog carrier or todemodulation with such a carrier.

While the proposed architecture is compatible with applying chopping inthe front-end, this is not mandatory. For instance, the sensing signalscan already have very good signal strength compared to possible offsets,as may be the case when using an electrical resolver for providing thesensing signals. Furthermore, flicker noise from the front-end can alsobe reduced by appropriate design (e.g. increasing the size of criticaltransistors).

ADC and Digital Filter

For applications which have rotations in the same direction over longtime periods (e.g. in motor control), the output angle in principlecontinuously increases. This might cause a problem when the output angleis represented by an analog signal with limited range. A solution tothis problem is to reset the analog signal, e.g. to zero, when someupper limit is reached. When the upper limit corresponds for instance toan output angle of 360°, a reset to zero then corresponds to performinga 360° phase jump to keep the analog signal into its limited range.However, if such operations are performed in the analog domain, they aresubject to various errors and imperfections. As described hereafter,this can be circumvented, e.g. by phase accumulation in the digitaldomain and performing the phase-wrapping in a much more ideal setting.

More generally, particular embodiments of the angle sensor have a loopfilter comprising digital filtering. The (total) loop filter then forexample comprises an analog filter, an analog-to-digital converter and adigital filter. Using digital filters has many advantages over analogcounterparts, e.g. in terms of transfer function accuracy, flexibilityand scalability with technology. The digital filter (63) may comprise anintegrator, for instance for accumulating a speed related signal (as isthe case in FIG. 2). The advantage of using a digital integrator is thatthese can have a nearly unlimited output range, thus providing a sensorarchitecture with multi-turn capabilities. Also integrators with limitedoutput range are very useful, e.g. providing an error-freeimplementation of the above-mentioned phase jumps. In its simplest formthe natural overflow of the digital integrator may provide an error-freephase-wrapping mechanism. As an example of the above it is possible tohave the digital integrator to have an output range of 800° where themost significant bits of the digital integrator define the number ofrevolutions and a high number of less significant bits define the anglewithin a single revolution with high accuracy, e.g. a 14 bit outputwhere two bits are used for the number of revolutions and 12 bits forthe fractional angle.

Arrangements for measuring an absolute angle using a multi-pole magnethave been worked out, e.g. in US2015/226581. These arrangements have theadvantage that they significantly decrease the sensitivity w.r.t. strayfields. It is an advantage of present invention that the sensor readoutarchitecture is compatible with the use of multi-pole magnets and/orstray-field insensitive sensor arrangements.

FIG. 7 shows an exemplary stray field robust arrangement for use with a6-pole magnet disclosed in US2015/226581, which is taken as an examplehere. The individual sense signals can in this situation be modeled as:

$\begin{matrix}{{{HE}_{k} = {A\; {\cos \left( {\theta_{i} - {k\frac{2\; \pi}{12}}} \right)}}}{{k = 0},{1\mspace{14mu} \ldots \mspace{14mu} 11}}} & (8)\end{matrix}$

With

θ_(i)=3×θ_(mech)  (9)

whereby θ_(mech) represents the absolute rotation angle of the 6-polemagnet. The main difference with expression (1) is that now the sensed(magnetic) angle θ_(i) is an integer multiple of the “mechanical” angleθ_(mech). Note that the relation between θ_(mech) and θ_(i) according to(9) assumes that for θ_(mech) equal to zero, the magnet and sensingelement configurations are properly aligned. If this is not the case, anextra offset angle can be added to the equation.

The sensor device of the present invention can provide a readout withimproved insensitivity to stray fields by using symmetric weights. Forthe above example, imposing the symmetry constraintsG_(k)=G_(k+4)=G_(k+8) for k=0, 1, 2, 3 leads to the desired result. Forinstance, because a common factor G₁=G₅=G₉ was chosen, the contributionof the signals from sensing elements S₁, S₂ and S₃ indicated in FIG. 6is the sum of these signals weighted by the common factor, and thereforethe influence of a uniform stray-field drops out (because of thesummation).

In general, when sensing elements are placed in a regular pattern andwhen the signals of a subgroup of these elements can be combined to makethe readout robust w.r.t. an interferer (e.g. an interfering externalmagnetic field), in the combiner circuit the weights/gains associatedwith the subgroup elements are chosen such that for all possible cases(i.e. all possible output angles) the subgroup signals are combined in away that retains the robustness w.r.t. the interferer. This includessituations where sensing elements are Hall plates spaced at the cornersof a regular polygon: signals from diametrically opposing plates (e.g. Xand X′) can be taken to have weights/gains with matched magnitudes and asign appropriate to block a uniform external field in a directionperpendicular to the Hall element.

Another advantage of present invention when combined with multi-polemagnets relates to the multi-turn capabilities of the loop. The sensordevice tracks θ_(i), even when increasing/decreasing beyond 360°. Takingthe 6-pole magnet again as an example, if (9) is valid at some point intime, the loop will from there on track θ_(i) even if θ_(i) goes beyond360°. As long as the loop is not thrown out of lock, the relation (9)remains valid. Therefore a measurement of the mechanical angle can beobtained as

θ_(mech)=⅓×θ_(o)  (10)

Note that without a means for making a correspondence between θ_(i) andθ_(mech) at some point in time, there remains an overall ambiguity onthe measured angles due to the 120° rotational symmetry of the magnet.This ambiguity can be resolved, e.g. by detecting (with other means)when θ_(mech) is in a relatively large but known range, e.g. between−60° and +60°.

Angle Quantizer

In the description the focus is mostly on the quantizer block (64)operating on an angle. It should be clear however that the quantizerblock (64) operating may also operate on a phase representative of a(generalized) position.

The angle quantizer block (64) associates with an input value an outputvalue from a finite set of allowed values. The selected output value maybe the allowed value closest to the input value. The simplest case iswhen the allowed values are uniformly distributed. When an ADC is usedin the loop, the angle quantizer block may be a purely digital function.A particularly simple form is based on identifying the “fractional bits”of the digital filter (63) output or a phase accumulator output, i.e.the bits which determine the angle as a fraction of a full circle. Theangle quantizer limits the number of levels of the output angle θ_(o)for covering a full circle, e.g. a number in the range 2 to 1024 or inthe range 4 to 64 or in the range 6 to 32 or in the range 8 to 16 levels(in each case limiting values inclusive).

The angle quantizer may also be an analog circuit having an analoginput, e.g. a comparator, a flash ADC or other types of Nyquist-rateADCs. In practice, this requires the output position range to be finiteand extra measures may need to be taken, e.g. for wrapping the inputangle of the angle quantizer to a basic range covering only 360°.

Embodiments of the position sensor which comprise a quantizer block (64)provide a digital output representative of the position, correspondingto the quantizer output. These embodiments therefore provide aposition-to-digital conversion. The number of bits taken for thequantizer (64) is influenced by two important factors. On the one hand,decreasing the number of bits reduces the complexity of the combinercircuit, making the position sensor easier to implement. On the otherhand, a high number of bits provides more resolution for the digitaloutput value of the (generalized) position. It will now be shown thatthese conflicting requirements can be alleviated by a “noise cancelling”technique in which the quantization noise introduced in the quantizer(64) of the position sensor is largely eliminated.

A scheme with noise cancelling according to the present invention isshown in FIG. 8. The quantizer (64) provides a digital output value (7)of the loop, denoted as D₁ in subsequent calculations. This quantizermay typically have a limited number of bits, e.g. for reducing thecomplexity associated with the combiner circuit (4). The quantizer (64)is in the digital domain and its input is provided by a digital loopfilter having a transfer function H_(d). The loop further comprises ananalog loop filter having a transfer function H_(a) followed by ananalog-to-digital converter. As the output of the analog loop filter issampled by the analog-to-digital converter, the transfer function H_(a)is taken as the discrete-time equivalent of the continuous-time transferof the analog loop filter. Determining such a discrete-time equivalentis well known in the field and can for instance be done by the c2dfunction provided in Matlab. The analog-to-digital converter provides adigital output, denoted as D₂ in subsequent calculations, which alsoprovides the input of the digital loop filter H_(d). The operation ofthe quantizers can be modelled as adding a quantization error to therespective quantizer input signal, the quantization error being definedas the difference between the output and the input of the quantizer. Twosuch extra “sources” can be identified in the system, being Q₁ and Q₂representing the quantization error of the quantizer (64) and theanalog-to-digital converter (62), respectively. Note that Q₁ may beconsidered a knowable quantity in the present system, since both theinput and the output of the quantizer (64) are in the digital domainand, hence, these signals can be digitally subtracted to obtain Q₁.Since perfect knowledge of Q₁ can be obtained, it becomes possible tocompensate for the effects caused by quantization noise Q₁ of thequantizer (64). A key question is of course how to do this and to whatextent this is possible when there are uncertainties in the system, suchas when one has only imprecise knowledge of the analog filter transferfunction H_(a). One possibility is to use the output D₂ of theanalog-to-digital converter circuit of the present invention, whenpresent, to largely eliminate the effects of Q₁. Some embodimentsdisclosed further on are capable of coping with imprecise knowledge ofthe analog filter transfer function H_(a), and even allow adapting totime-varying changes in this filter.

Using linear system analysis, the two digital outputs D₁ and D₂ in theabove system can be determined as a function of the input signal V_(i)and the two quantization error sources Q₁ and Q₂:

$\begin{matrix}\left\{ \begin{matrix}{D_{1} = {{{STF} \cdot V_{i}} + {{NTF} \cdot Q_{1}} + {H_{d} \cdot {NTF} \cdot Q_{2}}}} \\{D_{2} = {{\frac{STF}{H_{d}} \cdot V_{i}} - {H_{a} \cdot {NTF} \cdot Q_{1}} + {{NTF} \cdot Q_{2}}}}\end{matrix} \right. & (11)\end{matrix}$

In this expression the following transfer functions appear:

$\begin{matrix}\left\{ \begin{matrix}{{STF} = \frac{H_{a}H_{d}}{1 + {H_{a}H_{d}}}} \\{{NTF} = \frac{1}{1 + {H_{a}H_{d}}}}\end{matrix} \right. & (12)\end{matrix}$

These transfer functions are known in the context of Sigma-Deltamodulators as the signal transfer function (STF) and the noise transferfunction (NTF).

In accordance with the present invention, the two digital quantizeroutputs D₁ and D₂ go to a recombiner block where these are filtered bydigital filters A(z) and B(z), respectively, and then added. As detailedbelow, a delay compensation filter can optionally be provided as well.The thus obtained recombined output D_(out) can be expressed as:

D _(out)(z)

A(z)D ₁(z)+B(z)D ₂(z)  (13)

Substituting expression (11) in (13) it can be easily shown that if

$\begin{matrix}{\frac{A(z)}{B(z)} = H_{a}} & (14)\end{matrix}$

then

$\begin{matrix}{{D_{out}(z)} = {{A(z)}\left( {V_{i} + {\frac{1}{H_{a}(z)}Q_{2}}} \right)}} & (15)\end{matrix}$

Since Q₁ does not appear in the compensated output D_(out)(z), theproposed recombination has completely eliminated the contribution of Q₁.It is, however, shown later in this description that it is not strictlyneeded that the ratio of the transfer functions of the digital filtersA(z) and B(z) exactly equals H_(a).

In accordance with the present invention, other means to eliminate thequantization noise Q₁ can be applied. The output D₁ of the quantizer(64) has an additive term NTF(z)Q₁, as can for instance be seen fromexpression for D₁ in (11). The quantization noise Q₁ can be readilydetermined, e.g. by subtracting the input of the quantizer (64) from itsoutput, which are two signals readily available in the digital domain.This method to determine Q₁ is also used in FIG. 12 which will bediscussed below. Now, eqn. (12) provides an expression for the digitaltransfer NTF(z) in terms of the discrete-time equivalent H_(a)(z) of theanalog filter in the loop and the also known transfer H_(d)(z) of thedigital filter in the loop. Therefore, NTF(z) represents a known digitalfilter, which can be applied to the sequence of Q₁ values (e.g. obtainedfrom subtracting the input of the quantizer from its output), and theresult can be subtracted from the quantizer output (64) D₁ to arrive ata position output. The so obtained output D_(out)=D₁−NTF(z)Q₁ can beshown to be no longer dependent on the quantization noise Q₁, as can bestraightforwardly demonstrated based on eqn. (11). In reality the(discrete-time equivalent) transfer H_(a)(z) of the analog filter usedin determining NTF(z) may deviate from the true transfer because of theunavoidable variability of the analog filter e.g. with temperature. Inspite of this, it is easily attainable with the above describedcanceling method to produce a value D_(out) representative of a positionto be measured with reduced dependence on the quantization noise Q₁caused by the quantizer (64).

Above two distinct methods for noise-canceling have been described. Inboth cases there is a noise canceling block having two digital inputs:the quantizer output signal and a digital signal upstream of thequantizer. These two digital signals are combined in the noise cancelingblock in such a way that the combined signal provides an improved phasevalue representative for the position to be measured which is lessdependent on quantization noise caused by the quantizer. In the firstapproach the digital signal upstream of the quantizer used in the noisecanceling block is the output of the analog-to-digital convertercomprised within the loop filter. The combined signal is obtained byappropriately filtering both digital signals using digital recombinationfilters A(z) and B(z), and subsequently adding the outputs of therecombination filters. In the second approach, the digital signalupstream of the quantizer being used in the noise canceling block is theinput signal of the quantizer. The combined signal is obtained bysubtracting the two digital signals received by the noise cancelingblock, filter this (with an approximation of the NTF), and subtract thisfrom the quantizer output signal (also received by the noise cancelingblock). Based on the noise canceling methods disclosed in the presentinvention, a skilled person can in principle extend the approach to usea different digital signal appearing in the loop upstream of thequantizer, e.g. by using linear system analysis for deriving an equationsimilar to (11) for the digital signal appearing in the loop upstream ofthe quantizer, and then work out a linear combination of the two digitalinput signals of the noise-canceling block that eliminates thecontribution related to Q₁.

The advantage of the noise cancelling scheme is that the quantizer (64)may have a low resolution (i.e. a low number of bits), because thecorresponding quantization error Q₁ can be eliminated in the aboveexplained manner. This way, the number of feedback levels may berestricted, which can significantly simplify the design of the combinercircuit.

Another advantage offered by the invention can be understood byobserving the transfer of the input position to the digital output. Forthe digital noise-cancelled output, this transfer is A(z). When using D₁as digital output (without noise-cancelling), the signal transferfunction is STF(z) as defined in (12). This STF(z) is fixed by thechoices for the analog and digital loop filters H_(a) and H_(d),respectively. In contrast, it can be seen that (14) allows much freedomin selecting the recombination filters A(z) and B(z). It is thereforepossible to exploit this freedom to arrive at a more beneficial signaltransfer function A(z).

In general, the interconnection complexity of the combiner circuitreduces when the number of bits of the angle quantizer is lowered. Asmall number of bits implies a larger angle quantization error, and thestrategy to deal with angle quantization error as disclosed in presentinvention is therefore highly relevant.

An important quantity is the delay n—expressed as a number of sampleintervals (T)—between the digital feedback signal (D₁) and the digitaloutput of the ADC (D₂). Contributions to this delay may come from adelay in the feedback path, a delay associated with the integratorcircuit, the conversion time of the ADC, etc.

The more compact system-level diagram of FIG. 9 can then be derived forthe system as described. In the present example the action of the Ninput signals (2), the feedback signal unit (8) and the combiner circuit(4) produces an output signal (5) proportional to the sine of thedifference between input angle and the feedback angle corresponding withD₁. For studying transfer functions, the non-linear sin characteristicis neglected, that is, it is assumed sin x≈x with x sufficiently small.In the system level diagram the (total) delay n has been included in theanalog filter transfer function H_(a), while the feedback path and thequantizer (64) are idealized as having no delay. In the consideredexemplary case, the analog filter has a transfer function given by

${H_{a} = {K\frac{z^{- n}}{1 - z^{- 1}}}},$

with K a proportionality factor accounting for a multitude of scalefactors (such as the magnetic field strength, the Hall elementsensitivity, the time constant of the integrator, etc.).

In this exemplary embodiment the recombiner block uses the followingrecombination filters:

$\begin{matrix}\left\{ \begin{matrix}{{A(z)} = z^{- n}} \\{{B(z)} = \frac{z^{- n}}{H_{a}(z)}}\end{matrix} \right. & (16)\end{matrix}$

For this choice the condition (14) is obviously met. The reason why theextra delay z^(−n) is introduced, is to make the filter B(z) physicallyrealizable. For this example one obtains

${{B(z)} = \frac{1 - z^{- 1}}{K}},$

which represents a realizable FIR filter.

The choice A(z)=z^(−n) implies that the input signal is also delayed byn samples, which can be seen from (15). In case of angular sensorsoperating at high rotation speeds, this extra delay may cause noticeableangle errors, especially if n>1. In such cases, an optional delaycompensation filter may be added to the system whose purpose is tocompensate the delay n of the filter A(z). One example of a compensationfilter for compensating a delay n is:

$\begin{matrix}{{C(z)} = {1 + \frac{a\left( {1 - z^{- 1}} \right)}{1 - {\left( {1 - \frac{a}{n}} \right)z^{- 1}}}}} & (17)\end{matrix}$

One way to realize this filter is shown in FIG. 10. In (17) a denotes anextra parameter, typically between zero and one, to control thetrade-off between overshoot and high-frequency gain (which becomessmaller when a is lowered) on the one hand and on the other hand thesettling time (which becomes smaller when a is increased). When choosinga=n, the filter reduces to 1+n(1−z⁻¹), which is an intuitive way forcompensating delay based on a ‘speed’ estimate by differencing thesignal, but this choice has a very high overshoot and strongly amplifieshigh frequencies.

As explained before, the input signal transfer function has been changedto the transfer A(z) of the first recombination filter, possibly withthe delay thereof being compensated by a delay compensation filter. Thisis particularly interesting for angular sensors which provide an A/Dconversion of a possibly fast-changing angle, because it allowsimproving the dynamic response, e.g. by providing a faster stepresponse.

As also explained above, the position sensing device withnoise-canceling using the recombiner block as described may comprise adelay compensation filter to compensate for a delay introduced by thefirst recombination filter. However, also in other situations, a delaycompensation filter can be used advantageously. In general, additionaldigital filtering may be added to any of the exemplary embodiments ofpresent invention, e.g. for increasing the signal-to-noise ratio byreducing the (noise) bandwidth. If such filtering incurs extra delaythat cannot be tolerated in the envisioned application, this delay canbe compensated, e.g. using the above type of delay compensation filter.

FIG. 11 shows an embodiment of the position sensor according to theinvention wherein inner-loop noise shaping is applied. In this case, theanalog-to-digital converter (62) is implemented as a local feedback loopin which a second quantizer Q₂ is embedded in an internal feedback loop,having an analog loop filter with transfer function H_(b), and a localfeedback DAC. The dynamics of the local loop is dictated by its signaltransfer function H_(b)/(1+H_(b)). For a first-order filterH_(b)=z⁻¹/(1−z⁻¹) this signal transfer function is a simple delay z⁻¹.This simple delay can be directly incorporated in the total delay n ofthe global feedback loop. The delay may also be avoided by adding theoptional path shown on the figure. This optional path has the knowneffect that it makes the signal transfer function of the local loopequal to one. In such cases the local loop does not alter the dynamicbehavior of the global feedback loop. The main effect of the local loopis therefore that it applies noise-shaping to the quantization noise Q₂of the second quantizer. The equivalent quantization noise of the innerloop is Q₂/(1+H_(b)), which is at low to intermediate frequenciestypically considerably lower compared to the quantization noise Q₂ ofthe second quantizer used as a flash-ADC for analog-to-digitalconversion (62).

An additional advantage of the system with inner-loop noise-shaping isthat the non-linearity of the local feedback DAC is suppressed by theglobal loop. This means that multi-bit DACs can be applied with lessstringent conditions on the linearity.

It is not required that both quantizers Q₁ and Q₂ operate at the samerate. For instance, the inner feedback loop around Q₂ and possibly alsothe digital filter with transfer function H_(d) may be operated at ahigher rate compared to the global feedback loop. The quantizer (64)then subsamples the digital filter output H_(d).

In electronic systems process, supply voltage and temperature (PVT) areimportant sources of variability. The analog filter transfer H_(a) istypically affected by these PVT effects. For instance, a continuous-timeintegrator—a particular choice for the analog filter—can easily have atime constant which deviates 30% from its nominal design value. Evenlarger deviations may exist. For instance, in most position sensorsaccording to present invention, the magnitude of the weighted sum signal(5) depends on an amplitude of input signals, which typically depend onthe strength of the magnetic field that depends on the application. Inthe model of FIG. 9, therefore various variable factors exist whichaffect the gain of the analog filter transfer H_(a).

Some embodiments with adaptive schemes are now presented that canprovide effective cancellation of Q₁ even in view of variability of theanalog transfer function H_(a). First, the impact of mismatch isdiscussed.

The condition (14) links two digital filters to an analog transferfunction H_(a). Because the analog transfer function is subject tovarious sources of variability, the equation is in general not metexactly. In order to investigate the impact of mismatch between the realH_(a) on the one hand, and the nominal transfer used for the choice ofthe digital recombination filters H_(a,nom)=A(z)/B(z) on the other hand,the relative mismatch may be defined as

$\begin{matrix}{{\Delta (z)} = {\frac{H_{a}(z)}{{A(z)}/{B(z)}} - 1}} & (18)\end{matrix}$

Note that Δ(z) is identical zero if and only if the condition (4) ismet.

Consider, as an example, an uncertainty in the gain K of the analogtransfer H_(a), which deviates from the nominal value K_(nom) that isused for sizing the recombination filters A and B. Then, in this case(18) reduces to

${\Delta = \frac{K - K_{nom}}{K_{nom}}},$

i.e. Δ then represents a measure for the relative deviation of K fromK_(nom).

Taking into account a relative mismatch (8), an analysis as set outabove can be made. The compensated output D_(out) is then:

$\begin{matrix}{{D_{out}(z)} = {{A(z)}\left\{ {{\left\lbrack {1 + {{\Delta (z)}{{NTF}(z)}}} \right\rbrack \left( {V_{i} + {\frac{1}{H_{a}(z)}Q_{2}}} \right)} - {{\Delta (z)}{{NTF}(z)}Q_{1}}} \right\}}} & (19)\end{matrix}$

As expected, this equation reduces to expression (15) when Δ=0. From(19), it can be deduced that the noise-cancelled output signal D_(out)as provided by the present invention has a signal transfer function A(z)[1+Δ(z)NTF(z)]. A minor effect of a non-zero Δ is that it somewhatalters the transfer A(z) of the input signal V_(i) with an extra factor1+Δ(z)NTF(z). This can in most cases be neglected. In any case thesignal transfer function A(z) can be chosen more freely compared to the“classical” output D₁ which has a signal transfer function determined bythe loop filters.

More important for present application are terms in (19) related to Q₁.From the last term of the above expression, it can be seen that anon-zero A leads to leakage of Q₁ noise into the compensated outputD_(out). Luckily, this leaked noise is shaped by NTF(z), which is thenoise shaping created by both the analog filter H_(a) and the digitalfilter H_(d). When referred to the input, the leaked quantization noiseis given by Δ(z)NTF(z)/(1+Δ(z)NTF(z))Q₁. For the “classical” output D₁of the feedback loop as given by the first expression of (11), one hasthe input-referred contribution NTF(z)/STF(z)Q₁. The former ispreferably smaller in some sense than the latter, which can only be thecase when the relative mismatch Δ is restricted in some way. Thefollowing theorem can be proven:

If for a definite frequency f one has that

|Δ(z)|<1/(|STF(z)|+|NTF(z)|) with z=exp(j2πf)  (20)

then the magnitude of the input-referred Q₁ noise at frequency f issmaller for the noise-cancelled output signal D_(out) compared to themagnitude of the input-referred Q₁ noise when using the “non-cancelled”output D₁. Note that (20) is not a necessary condition, but merelyprovides a convenient sufficient condition. Fortunately, equation (20)is in most cases not very restrictive and relative mismatches A in theorder of a few percent, even 10% and more are likely to agree with (20).Furthermore, if (20) is met for all frequencies f, it is guaranteed lessinput-referred Q₁ noise is present in D_(out) compared to D₁. However,even if expression (20) would be violated for some frequencies, it isstill possible that the integrated power of the leaked quantizationnoise is smaller than the integrated power of the quantization noise Q₁present in the “non-cancelled” output D₁. In other words, if there ismore Q₁-related noise at some frequencies this can be offset by lessnoise being present at other frequencies. Therefore, it can be concludedthat a very broad range of recombination filters A(z) and B(z) existwhich result in the “noise-cancelled” output D_(out) being lessdependent on the quantization noise Q₁ compared to the “none-cancelled”output D₁ of the feedback loop. The latter may be quantified bycomparing the signal-to-noise ratio (SNR) of D_(out) to the SNR of the“non-cancelled” output D₁. While the recombination filters A(z) and B(z)may be chosen starting from (14) and taking into account the designfreedom indicated by (18) and (19), other design procedures are alsopossible. For instance, one may A(z) and/or B(z) to be parameterizedfilters, e.g. an FIR filter with variable coefficients, and thendetermine the optimum filter parameters which maximize the SNR ofD_(out). When the optimum SNR of D_(out) turns out to be lower than theSNR of D₁, a choice is obtained for A(z) and B(z) that by constructionprovides a noise-cancelled output D_(out) being less dependent on thequantization noise Q₁ compared to the “non-cancelled” output D₁ of thefeedback loop. Such an optimization approach also provides extraflexibility for introducing a signal transfer function (corresponding tothe recombination filter A(z), as explained above) of a preferred form.

In another embodiment the gain-variability of the analog filter H_(a) iscounteracted by introducing a compensating scale factor, for instance inthe second recombination filter. This approach is illustrated in FIG.12. In this embodiment the second recombination filter (22) comprises aprogrammable gain G, which allows scaling a signal in accordance with again control signal. The gain control signal is generated by a gaincontroller unit (3) which receives the output of the recombiner block(9) and the quantization noise Q₁. The quantization noise Q₁ can forinstance be calculated by subtracting the input of the quantizer (64)from its output, both input and output being signals in the digitaldomain. The gain controller unit (3) comprises filtering means D(z) (31)and E(z) (32) for filtering its input signals, a multiplier (33) formaking the product of these filtered signals and an adaptationcontroller (34) which adapts its output until its input signal becomeson the average zero.

Equation (19) provides the basis for understanding how the above andother more general adaptive schemes operate. For this, expression (19)is rewritten in the following more compact form:

D _(out) =A(z)θ_(i) +A(z)/H _(a)(z)Q ₂−Δ(z)A(z)NTF(z)Q ₁  (21)

For reasons of clarity, the effect Δ has on the signal transfer functionis disregarded. Note that this approximation is not strictly needed,because the adaptive scheme makes Δ small, so the approximation becomesmore accurate over time. The three terms in (21), corresponding toθ_(i), Q₁ and Q₂ respectively, may be considered statisticallyuncorrelated. Optionally a filter D(z) may now be applied to theanalog-to-digital converted output signal D_(out) e.g. for reducing thesignal-related component θ_(i). For instance, when θ_(i) occupiesrelatively low frequencies, as is typically the case in an angularsensor, D(z) could be a first order difference 1−z⁻¹ or a second orderdifference (1−z⁻¹)² which would largely eliminate the input signalcomponent. The filtered output signal (i.e. D(z)D_(out)) is then givenby eqn. (11) multiplied with D(z). The last term of the filtered outputsignal is then of the form Δ(z)E(z)Q₁ with E(z)=D(z)A(z)NTF(z). BecauseA(z), D(z) and also NTF(z) are known digital filter (see equation (12)for the NTF), E(z) is also a known filter. Now Q₁ is a calculabledigital signal, and this can be filtered with the filter E(z). Thefiltered signals D(z)D_(out) and E(z)Q₁ may then be multiplied, as isdone in FIG. 12. The output of this multiplier provides a measure of therelative mismatch Δ (in a statistical sense). This multiplier output maybe considered an error signal of the adaptation loop (which is to beminimized). It can indeed be shown that the expected value of themultiplier output is proportional to Δ, because the cross-terms in theproduct which relate to θ_(i) and Q₂ average to zero (since θ_(i) and Q₂are uncorrelated to Q₁). Therefore, in accordance with presentinvention, the recombination filter A(z) and/or B(z) may be taken asadaptive filter. The parameters of the adaptive filter(s) may then beadapted in accordance to methods known in the art for minimizing theerror signal, e.g. minimizing this error signal in a mean squared sense.

While the invention has been illustrated and described in detail in thedrawings and foregoing description, such illustration and descriptionare to be considered illustrative or exemplary and not restrictive. Theforegoing description details certain embodiments of the invention. Itwill be appreciated, however, that no matter how detailed the foregoingappears in text, the invention may be practiced in many ways. Theinvention is not limited to the disclosed embodiments.

Other variations to the disclosed embodiments can be understood andeffected by those skilled in the art in practicing the claimedinvention, from a study of the drawings, the disclosure and the appendedclaims. In the claims, the word “comprising” does not exclude otherelements or steps, and the indefinite article “a” or “an” does notexclude a plurality. A single processor or other unit may fulfil thefunctions of several items recited in the claims. The mere fact thatcertain measures are recited in mutually different dependent claims doesnot indicate that a combination of these measures analog filter (61),especially when it comprising one or more cannot be used to advantage. Acomputer program may be stored/distributed on a suitable medium, such asan optical storage medium or a solid-state medium supplied together withor as part of other hardware, but may also be distributed in otherforms, such as via the Internet or other wired or wirelesstelecommunication systems. Any reference signs in the claims should notbe construed as limiting the scope.

1. A position sensing device for measuring a position, comprising aplurality of sensors arranged to produce sense signals each being afunction of an input phase representative of a position to be measured,a combiner circuit arranged to generate an error signal by combiningsaid sense signals according to an array of weight factors, a processingblock comprising a loop filter to filter said error signal, and arrangedfor deriving from said filtered error signal a phase valuerepresentative of said position and for outputting said phase valuerepresentative of said position, a feedback loop comprising a feedbacksignal unit arranged for receiving said output phase value and foradjusting based on said received output phase value said array of weightfactors, so that said weight factors are a function of said output phasevalue.
 2. The position sensing device as in claim 1, wherein saidprocessing block comprises a quantizer arranged to receive said filterederror signal and to generate said phase value representative of saidposition.
 3. The position sensing device as in claim 1, wherein saidloop filter comprises an analog filter arranged to receive said errorsignal.
 4. The position sensing device as in claim 1, wherein said loopfilter comprises an analog-to-digital converter and a subsequent digitalfilter.
 5. The position sensing device as in claim 4, wherein said loopfilter comprises a cascade of an analog filter, the analog-to-digitalconverter and the digital filter and wherein said processing blockcomprises a quantizer arranged to receive said filtered error signal andto generate said phase value representative of said position.
 6. Theposition sensing device as in claim 1, wherein said feedback signal unitcomprises an angle-to-gain conversion block arranged for receiving saidoutput phase value.
 7. The position sensing device as in claim 6,comprising a digital gain control unit arranged to adapt said weightfactors.
 8. The position sensing device as in claim 7, wherein saidarray of weight factors is implemented by switchably connectedcomponents in said digital gain control unit or by an analogmultiplexer.
 9. The position sensing device as in claim 1, wherein saidsensors are magnetic sensors arranged for measuring an angle of amagnetic field.
 10. The position sensing device as in claim 1, whereinsaid plurality of sensors comprises at least three sensors arranged toproduce sense signals each being a different function of an input phaserepresentative of a position to be measured.
 11. An arrangementcomprising a position sensing device as in claim 1 and a multi-polemagnet.
 12. A position sensing device for measuring a position,comprising a plurality of sensors arranged to produce sense signals eachbeing a function of an input phase representative of a position to bemeasured, a combiner circuit arranged to generate an error signal bycombining said sense signals according to an array of weight factors, aprocessing block comprising a loop filter to filter said error signal,said loop filter comprising a cascade of an analog filter, ananalog-to-digital converter and a digital filter, and further comprisinga quantizer arranged to receive said filtered error signal and toproduce from said filtered error signal a quantizer output signal, afeedback loop comprising a feedback signal unit arranged for receivingsaid quantizer output signal and for adjusting based on said receivedquantizer output signal said array of weight factors, so that saidweight factors are a function of said quantizer output signal, a noisecanceling block arranged for combining said quantizer output signal witha digital signal upstream of said quantizer such that the combinedsignal provides an improved phase value representative of said positionand has a reduced dependence on quantization noise caused by saidquantizer.
 13. The position sensing device as in claim 12, wherein saidnoise canceling block comprises a first recombination filter arranged toreceive said quantizer output signal, a second recombination filterarranged to receive a digital signal output by said analog-to-digitalconverter and an adder circuit for adding outputs of said first and saidsecond recombination filter, said first and said second recombinationfilter being selected to obtain an phase value representative of saidposition with reduced dependence on quantization noise caused by saidquantizer.
 14. The position sensing device as in claim 13, wherein saidanalog filter of said loop filter has a transfer function substantiallyequal to the ratio of said first recombination filter's transferfunction and said second recombination filter's transfer function. 15.The position sensing device as in claim 13, wherein said firstrecombination filter and/or said second recombination filter areadaptive.
 16. The position sensing device as in claim 15, wherein saidfirst recombination filter and/or said second recombination filter has aprogrammable gain.
 17. The position sensing device as in claim 13,wherein said quantizer has a lower resolution than saidanalog-to-digital converter.
 18. The position sensing device as in claim13, comprising a delay compensation filter to compensate for a delay.19. The position sensing device as in claim 13, wherein saidanalog-to-digital converter is a Sigma-Delta modulator comprising asecond quantizer embedded in an internal feedback loop containing afurther analog filter and a feedback digital-to-analog converter. 20.The position sensing device as in claim 13, wherein the firstrecombination filter and/or second recombination filter are FiniteImpulse Response filters.